Geodesic
The Dirichlet problem in a~domain with a~slit
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 208-221

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A basis of harmonic wavelets is constructed in an elliptic ring and its approximation properties are investigated. The obtained results are used to analyze the behavior of a boundary-value Dirichlet problem under the contraction of the inner boundary of the ring to a segment.
Keywords: harmonic wavelets, Dirichlet problem, domain with a slit, asymptotic expansion, approximation error. 
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     author = {Yu. N. Subbotin and N. I. Chernykh},
     title = {The {Dirichlet} problem in a~domain with a~slit},
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Yu. N. Subbotin; N. I. Chernykh. The Dirichlet problem in a~domain with a~slit. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 1, pp. 208-221. http://geodesic.mathdoc.fr/item/TIMM_2009_15_1_a16/